Question

微积分题目：∫上限5下限1 x/√2x-1 dx

Answer 1

√2x-1=t x=5时,t=3 ; x=1时,t=1

t^2=2x-1

x=(t^2+1)/2

dx=dt

代入原式：

＝f (1, 3) (t^2+1)/(2t)dt

=f(1,3) (1/2t+1/(2t))dt

=1/4t^2+1/2lnt (1,3)

=(9/4+1/2ln3)-1/4

=2+1/2ln3